AIAA 2001-4135
A Sensor-lnd.ependent GustHazard Metric
Eric C. Stewart
NASA Langley Research Center
Hampton, VA
AIAA Atmospheric Flight Mechanics ConferenceAugust 6-9, 2001 / Montreal, Canada
For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500. Reston. VA, 20191-4344
https://ntrs.nasa.gov/search.jsp?R=20010097310 2020-04-09T01:05:54+00:00Z
AIAA 2001-4135
A SENSOR-INDEPENDENTGUST HAZARD METRIC
Eric C. Stewart*
NASA Langley Research CenterHampton, VA 23681-2199
Abstract
A procedure for calculating an intuitive hazard
metric for gust effects on airplanes is described. Thehazard metric is for use by pilots and is intended to
replace subjective pilot reports (PIREP's) of theturbulence level. The hazard metric is composed of 3numbers: the first describes the average airplane
response to the turbulence, the second describes the
positive peak airplane response to the gusts, and thethird describes the negative peak airplane response to
the gusts. The hazard metric is derived from any timehistory of vertical gust measurements and is thus
independent of the sensor making the gustmeasurements. The metric is demonstrated for one
simulated airplane encountering different types of gustsincluding those derived from flight data recordermeasurements of actual accidents. The simulated
airplane responses to the gusts compare favorably withthe hazard metric.
Nomenclature
A
Ar
A"
non-dimensional gust amplitude, g's
dimensional gust amplitude over computation
interval r, ft/sec
non-dimensional gust amplitude over
computational interval r, -- g'sw 1
measured gust amplitude in positive direction,
ft/sec
*Aerospace Engineer, Senior Member AIAA
Copyright © 2001 by American Institute ofAeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17, U.S.
Code. The U.S. Government has a royalty-free
license to exercise all rights under the copyrightclaimed herein for Government Purposes. All
other rights are reserved by the copyright owner.
I
A+
2
Ar
(7+).
a cg
aaft
0.n
0.n
0"4.0
measured gust amplitude in negative direction,
ft/sec
measured gust amplitude in positive direction,
A'+--, g'sw,
measured gust amplitude in negative direction,
A'_--, g's
w I
estimated gust amplitude required to produce
lg acceleration for a computational interval r,
g's
maximum measured gust amplitude in positive
direction using a computational interval of rseconds (figure 3), g's
minimum measured gust amplitude in negative
direction using a computational interval of rseconds (figure 3), g's
maximum estimated gust amplitude in positive
direction using a computational interval of r
seconds (figure 3), g's
minimum estimated gust amplitude in negative
direction using a computational interval of rseconds (figure 3), g's
change in acceleration at the center of gravity
(positive upward), g's
change in acceleration at the aft passenger
cabin (positive upward), g's
running standard deviation of acg over a
computational interval of 4 seconds, g's
average value of o"n over reporting interval,
g's
standard deviation of vertical gust velocity
over a 4-second computational interval, fps
-l-
American Institute of Aeronautics and Astronautics
0"4.0 standard deviation of non-dimensional vertical
gust velocity over a 4-seconds computational
0"4.0interval, --, g's
w I
r computation interval (also called rise time),
0.25, 1.0, and 4.0 seconds in example
W airplane weight, Ibs
wg vertical gust velocity (positive upward), fps
p density of air, slug/ft 3
V true airspeed, fps
S wing area, ft 2
t time, seconds
CL, _ lift curve slope, per radian
w t gust amplitude of a step input that will cause a
2_p ), fps1g acceleration ( VSCL., _
HM composite hazard metric,
[ HM,_ HM+ HM_ ], g's ( Read as
"' HMo ' g's continuous turbulence, with
peaks to plus' HM÷ ' g's and minus ' HM_ '
g's")
HM,. hazard metric for peak gusts using a
computation interval of r seconds, g's
HMr_.k peak hazard metrics HM÷ and HM_,
g's
HM÷ component of composite hazard metric due to
peak positive gusts, g's
HM_ component of composite hazard metric due to
peak negative gusts, g's
HM,_ component of hazard metric for sigma level of
turbulence, g's
Introduction
The National Aeronautics and SpaceAdministration has initiated the Aviation Safety
Program to reduce the aircraft accident rate by 80% inl0 years. One part of the program is aimed at reducingthe injuries and deaths caused by extreme turbulenceencounters. Airline experts report and the analysis of
Flight Data Recorder (FDR) data indicate that theseextreme events are caused by large, discrete gusts in thevertical direction, reference 1. The typical gust
encounter that induces serious injuries lasts only a fewseconds and is surrounded by relatively calm
conditions. The (unbuckled) victim is usually thrown
to the ceiling when the airplane momentarilyexperiences less than 0 g's vertical acceleration. Themost severe injuries occur when the acceleration returns
to normal positive values and the victim falls back tothe floor or, worse yet, on the seat backs or arm rests.
Usually the only damage to the airplane is confined to
the airplane interior and is caused by the impact ofunsecured objects and people with the cabin ceiling andoverheads.
One approach to reducing the turbulenceaccident rate is to develop new or improved turbulence
warning and avoidance sensors such as enhancedairborne radars or iidars, reference 2. However, aclearer definition of the turbulence characteristics thatcause the accidents is needed so that the new sensor
outputs can be made to accurately reflect thesecharacteristics. Past turbulence metrics have had one or
more deficiencies. For example, the turbulence metric
described in reference 3 is a measure of the eddy
dissipation rate, an "average" meteorological parameterunknown to most pilots. The metric described inreference 4 is a running average of the square of the
vertical gust velocity. Neither metric is a directmeasure of the peaks of dangerous discrete gusts that
are of primary interests to pilots, reference 5. Inaddition, these metrics do not discriminate between
positive gusts and the more dangerous negative gusts.Finally, since both are measures of only turbulencecharacteristics, they need to be multiplied by the
appropriate airplane transfer functions to translate theminto more useful information for pilots flying different
airplanes at different airspeeds in the same turbulencefield. This is not to say, however, that the averagevalue of the turbulence is of no interest. For the
majority of airline operations in turbulence, theturbulence has a relatively low level and appears to bemore or less continuous. Therefore, any metric that isuseful in all conditions must reflect the "average" value
of continuous turbulence as well as the peaks of the
discrete gusts.The primary purpose of this paper is to define
the discrete-gust components of the hazard metric as afunction of the first-order, fundamental parameters thatdetermine airplane gust response. A procedure for
calculating the numerical values of these components ofthe hazard metric from measurements of vertical gust
velocities is discussed. (The method of measuringthese velocities is beyond the scope of this paper). The
composite hazard metric, which also includes anaverage component for continuous turbulence, is
intended to replace Pilot Reports (PIREPS) which aresubjective, airplane-dependent estimates of turbulenceintensity as described in the Aeronautical Information
Manual (AIM), reference 6. Since the present metric isbased on the characteristics of turbulence that are the
-2-
American Institute of Aeronautics and Astronautics
rootcauseof airplane turbulence response, it can beused as the basis for developing sensor-dependenthazard metrics.
Theoretical Basis
Previous work, reference 7, has shown that the
rise time of discrete gusts as well as their amplitudeaffects the theoretical severity of a gust encounter. For
example, if an airplane gradually encounters a givenamplitude gust, its response is much smaller than if the
airplane encountered the same amplitude gust in a muchshorter period of time. (The rise time is equal to the
spatial dimension of the gust divided by the trueairspeed of the encountering airplane. In the
description of the hazard metric algorithm below, the"computation interval" is equal to the rise time). Thereis another class of parameters describing thecharacteristics of the encounter airplane that affects the
airplane response, but these parameters are readilyavailable on the data bus of most modem commercial
airliners.
Desired Characteristics of Hazard Metric
A measure of the potential gust hazard toairplanes (hazard metric) that is intuitively obvious is
needed. For example, a metric similar to the wind
direction and magnitude information an airport trafficcontroller gives to a pilot approaching an airport wouldbe useful. In-flight turbulence could be reported as:"Five knots continuous with peaks to plus 10 knots andminus 15 knots." The value of the continuous
turbulence can be a simple running calculation of the
standard deviation (sigma) of the vertical gust velocityand is related to ride comfort more than safety. It,therefore, is not the focus of this paper and the NASA's
aviation safety program, but is included for
completeness. The sigma value of the vertical velocityis closely related to the cube root of the eddy
dissipation rate calculated in the in-situ turbulence
algorithm described in reference 3. The cube root of
the eddy dissipation rate (in meters2/3/second) is more
meaningful to meteorologists, and the sigma level ofthe turbulence (in knots or other velocity units) is more
meaningful to pilots as a measure of the continuousturbulence and ride comfort.
For the large discrete gusts that cause
accidents there may be no consistent relationshipbetween the sigma value of the turbulence and the peakvalues. The peak values of the gusts are the metrics of
interest to pilots from a safety standpoint, reference 5.
But for the peak values to be of real value they mustalso reflect the rise time or the spatial extent of the
gusts. In addition, reporting the turbulence levels inknots (or other velocity units) would require the pilot to
mentally translate those numbers into a projectedresponse of his airplane at the current airplane
configuration and flight condition. Although a similarmental translation is currently required of pilots for the
above-mentioned tower-reported wind conditions, amore useful hazard metric would automatically
translate the gust velocities into response units such as
g's. This translation could be easily accomplished withexisting on-board computing capability and parameters
already available on the airplane's data bus such as theairplane's weight, airspeed, and altitude. Theturbulence could then be displayed to the pilot on
his/her console message center as (for example): "Two-
tenths g continuous, with peaks to plus five-tenths andminus eight-tenths g's." This is the type of hazardmetric described herein. It actually consists of three
numbers, HM,,, HM+, and HM_, but will be
referred to in the singular.There is another desired characteristic of the
hazard metric that is implicit in the above discussion.That is, the hazard metric is defined over a relatively
long period of time and reported at the end of this
period. This is desirable from the pilot's standpointbecause of his limited capability to process largevolumes of data. It is also desirable from the standpoint
of data transmitting and receiving bandwidthsrequirements. That is, the datalink capacities oncommercial airliners will limit the frequency that
turbulence information can be reported or received. Ifbandwidth were not a factor, the complete time history
of gust velocity measurements could be applied to an
airplane-specific, configuration-specific, transferfunction on every airplane. This approach would
provide a more exact prediction of the airplane'sresponse than the approximate response functionincorporated in the present hazard metric.
Algorithm Description
Since this is a description of a sensor-
independent hazard metric, it is assumed herein that a
time history of the vertical gust velocity is available.The method used to make these measurements is not
considered; see reference 2 for example measurements.
Only the translation of these assumed gust velocitiesinto a meaningful metric for pilots is discussed. The
complete algorithm, shown in figure 1, is described indetail in the following discussion. The first part of thealgorithm is the calculation of the sigma component ofthe hazard metric described by the upper leg of the flow
diagram. The sigma level 0''40 (t) is calculated for a
fixed interval of time. The preliminary suggested
3
American Institute of Aeronautics and Astronautics
computationintervalforthiscalculationis4secondsalthoughtheexactintervalisnotimportantsincethevalueswillbeaveragedlateroverthemuchlongerreportinginterval.Theinstantaneoussigmalevels0''40 (t) in ff/sec are divided by w I to produce the non-
dimensional sigma levels 0"4.0(t), in g's. The first
component of the hazard metric for the sigmaturbulence is simply the average value of the 4-second
running sigma level 0-4.0 over the reporting interval
(suggested length of 2 minutes).
HM o = 0---4.o (I)
The second part of the algorithm is the calculation of
the peak components of the hazard metric described bythe lower leg of the flow diagram. The first step in this
leg is the calculation of the incremental gust amplitudesas illustrated in figure 2. The word "incremental"
should be emphasized in the preceding sentence. Theincremental amplitudes are calculated relative to the
instantaneous value of the vertical gust velocity at thebeginning of each computation interval. The figureshows calculations at two different measurement times
t_ and t 2 . At each measurement, three least squares
lines containing 0.25 seconds, 1.0 second, and 4.0
seconds of data are calculated from the wg values
supplied from the turbulence sensor at some given datarate. (For example, 100 samples, second). Only the
slope of these lines is of interest since it is only theslope, and not the intercept, that affects the gust
response of the airplane. The values of the slopes foreach line are kept in separate bins for each computationinterval (rise time), r, (0.25 seconds, 1.0 second, and 4.0seconds in the above example). These three binscontain all the instantaneous values over a fixed interval
of time (preliminary suggested reporting interval is 2minutes). The values in each bin over the 2-minute
interval are then multiplied by their respective
computation interval (0.25, 1.0, or 4.0 seconds in theexample) to produce the incremental gust amplitudes inthe units of velocity--see typical incremental gust
#
amplitude A l0 (tl) for the measurement at t = t I in
figure 2. The dimensional gust amplitudes A_ (t) in
ff/sec are then divided by w 1 , the level of a step-input
vertical gust that will produce an acceleration of 1 g, to
produce the non-dimensional gust amplitudes A, (t) in
g's.
The next step in the calculations for peak hazard metriccomponents is to scale the non-dimensional gust
amplitudes A r (t) to approximate the airplane response
to different gust rise times. The result of this
calculation is HM, (t), the estimate of airplane
response due to gusts with lengths corresponding to r =
0.25, 1.0, and 4.0 seconds. The equation used was
HM_ = -A,(t)/ 2, (2)
where
-4r = 1 + r with r = 0.25, 1.0, and 4.0. (3)
^
The equation for A r is an approximation for the l-g
acceleration contour presented in figure 11 of reference
7. Further research may be needed to define a more
representative equation for the whole commercial fleet.The last step in the process is to determine the
maximum and minimum values of HMr to produce
the peak hazard metric components, HM+ and
HM.
HM + = ( HM , ) max and
HM_ = ( HM, )ram (4)
It should be noted that the dimensional sigma
level 0-'4.0 (t) and the gust amplitudes .,zl_(t) may be
useful to meteorologists for producing various weather
products. However, the emphasis here is on a hazardmetric for pilots for use in the cockpit in place ofcurrent PIREP's.
A graphical depiction of the logic involved incalculating the peak components of the hazard metric is
presented in figure 3 for an assumed example. As canbe seen from figure 3, the lines of constant +/- 1 gacceleration (corresponding to equation (3)) reflect thefundamental characteristic that larger gust amplitudes
are required to produce the same acceleration level forlonger rise times. The figure also illustrates the logic
for calculating values of the peak hazard metric
components HM , and HM_ .
For the present example of three rise times, the
6 peak non-dimensional gust amplitudes in thereporting interval can be compared with theircorresponding values on the lines of constant +/- 1 gacceleration. The positive gust amplitude that is largestrelative to its corresponding value on the +lg line will
be the "reported" positive peak hazard metric
component. A similar interpretation can be applied to
4
American Institute of Aeronautics and Astronautics
thenegativepeakcomponent.Ofcourse,theseoperationsareactuallycarriedoutinthealgorithmbyequations(1)thru(3)for HA[+ and HM_. In the
example shown in figure 3, (A+)10 is the largest
relative positive gust, and (A)40 is the largest
relative negative gust.For this paper, a distinction is made between
positive and negative gusts since negative gusts areconsidered more dangerous because they can cause
people to rise offthe floor or their seats. However,further research may indicate that only the largest
absolute peak hazard metric (or only the negativehazard metric) is needed. The sigma hazard metric
component will probably be necessary no matter whichpeak hazard metric component is used.
The three rise times used in this paper
correspond to different spatial dimensions of the
turbulence depending on the true airspeed of theairplane. For a typical cruise speed of 800 ft/sec, the
corresponding spatial dimensions are 200 ft, 800ft, and3200 ft. The present values of rise time are preliminaryand further research may be needed to establish final
values. In addition, more than three different values ofrise time could be used for finer rise time resolution or
a wider range of rise times.
Simulated Cases
Sample calculations were made to illustrate theapplication of the hazard metric using the preliminaryvalues of the defining parameters. The one exception to
the suggested preliminary values is the 2-minute
reporting interval because the data did not exist for thatlength of time. In these calculations, various gustshapes were used as input to the longitudinal mathmodel for the 140,000 lb transport airplane described in
reference 7. The simulated airplane responses to these
gust shapes were then recorded and the maximum andminimum accelerations at the center of gravity weredetermined. The hazard metric was, on the other hand,
calculated solely from the input gust shapes and the
gust parameter w 1 as described above. The results of
these calculations are shown in the following figures.
The simulations were run using a time increment of.01seconds. The effect of the values of the time increment
on the comparison was not investigated.
Discrete Gust Example The results of the calculations
for a gust profile derived from the flight recordermeasurements of an actual accident are presented in
figure 4. The gust profile is representative of a discretegust that causes accidents. The 4-second running sigma
calculation of the vertical gust velocity, o'40, begins
with a relatively large value because it includes the first
4 seconds of the data in figure 4. When o-4. 0 is non-
dimensionalized by w I and then averaged over the 14
seconds of available data, the sigma hazard metriccomponent is about twice the averaged simulated c.g.
acceleration (1.18 g's compared to 0.62 g's), figure 5.Thus, the sigma hazard metric component does not
correlate well with the simulated response for a discretegust. This result was expected since the sigma hazard
metric component is designed for low-level continuousturbulence and not discrete gusts. In addition, it should
be remembered that for this example, the averaging
time for HM,_ was only 14 seconds rather than the
suggested 2 minutes for an operational algorithm. If2minutes of flight data were available, the averaged
values o'---n and HM,_ would probably be much smaller
than in this calculation because of the apparent limitedspatial extent of this particular discrete gust. In fact, if
the averaging interval (reporting interval) were much
longer, o'---_and HM,, would approach zero even
though there are very dangerous peaks in the gust.
These peaks are captured by the peak hazard metriccomponents described next.
The dimensional gust amplitudes, A' 's, for
the peak components of the hazard metric are alsopresented in figure 4. The largest (absolute)dimensional gust amplitude for this discrete gust is forthe 4-second rise time. However, the calculations
shown in figure 5 indicate that when the amplitudes are
adjusted for the response characteristics of the airplane(using equation (3)), the resulting hazard metric for the
1.0-second rise time has the largest values (+1.29 g'sand -2.50 g's). These values compare reasonably wellto the largest simulated accelerations at the center of
gravity of 1.73 g's and -1.87 g's. Although thecomparison might be improved by using different risetimes, the comparison for other gust profiles might be
degraded. A large variety of gust shapes must beexamined to see which rise times, etc give the bestoverall correlation. Continuous Turbulence Example
Continuous Turbulence It is instructive to examine the
characteristics of the 3 hazard metric components forcontinuous turbulence. The dimensional parameters for
Dryden turbulence (sigma level = 30 fps andcharacteristics scale length of 1750 feet) are shown in
figure 6. The 4-second running sigma level, o'40 is
relatively constant as it should be for continuousturbulence. In addition, the sigma hazard metric
component, HM_, compares favorably with the
averaged sigma simulated acceleration, o', ,(I.47 g's
-5-
American Institute of Aeronautics and Astronautics
and 1.29 g's respectively in figure 7). This result was
expected since the sigma hazard metric component wasdesigned for continuous turbulence such as this.
The 3 peak amplitude traces ( A'25, Ai0,
A'4o in figure 6) show that this part of the algorithm
effectively filters the gust velocities with the longer rise
times corresponding to longer filter time constants. Forthis turbulence, the peaks of the incremental gust
amplitudes are practically equal for rise times of 0.25seconds and 1.0 seconds while the gust amplitudes forthe 4.0-second rise time are much smaller. When the
dimensional amplitudes arc adjusted for the airplane
response, the peak hazard metric componentsfor the 0.25-second rise time are the largest, figure 7,rather than those for the 1.0-second rise time for the
discrete gust example. This result reflects the high
frequency content of the Dryden turbulence. The finalvalues for the peak hazard metric components are +4.71
g's and -3.09 g's. These values do not compare asfavorably with the simulated peak c.g. accelerations
(2.59 g's and -3.26 g's) as did the previous values forthe discrete gusts. However, more examples are neededto draw firm conclusions. Another noticeable
difference in the calculations in figure 7 is the high
frequency (3 Hz) response in the acceleration at the aftcabin location. This response is due to the first-
fuselage-bending mode being excited by the highfrequency components of the Dryden turbulence. The
present hazard metric does not account for structuralresponses, but as shown in reference 3 high frequencyaccelerations are not likely to cause passenger injuries.
Collected Results: Twelve additional gust wave shapes
were investigated in addition to the two examplesshown above. That is, mountain rotor wave shapes
with 4 different amplitudes and gust lengths weresimulated using the expression described in reference 7.
Two additional discrete gusts from actual airplaneaccidents were simulated, as were four l-cosine gusts,and two additional Dryden turbulence fields with
different sigma levels and scale lengths. The results ofthese calculations are summarized in figures 8-I0. The
agreement between the peak hazard metric components,figure 8, is acceptable for most of the gust shapes withthe poorest agreement for the continuous Drydenturbulence as expected. Generally, the largest
disagreement is in a conservative direction; that is, the
peak hazard metric over-predicts the actualaccelerations.
Although the hazard metric presented here was
designed to predict the acceleration at the center ofgravity, a comparison of the peak hazard metriccomponents and the acceleration at the aft passenger
cabin are compared in figure 9. The biggest differencebetween figures 8 and 9 is that the simulated
/
accelerations in the aft cabin, _,a,a }t,,,ak ' are shifted to
larger absolute values especially for the Dryden
turbulence. This result is to be expected since theairplane's rigid-body pitching motion and the structural
response tend to increase the acceleration at the aftcabin compared to the acceleration at the center of
gravity. But as mentioned earlier, the high-frequencyaccelerations due to the structural mode are not as
likely to cause passenger injuries as are the lower rigid-body accelerations, reference 7.
The sigma component of the hazard metric is
compared to the simulated sigma acceleration at thecenter of gravity in figure 10. As expected the
agreement is good for the Dryden turbulence but poor
for the discrete gusts. This result is the opposite of theresult shown in figure 8. Thus, these two figures showthat the sigma component and the peak components
complement each other for different types ofturbulence. It should be emphasized that the above data
are for simulated airplane responses. As shown inreference 7, the actual airplane response in the NTSB-
reported data were sometimes much larger than thesimulated responses. The reason for this discrepancy
was most probably due to either transients when theauto-pilot disconnected or out-of-phase inputs by the
pilot. No hazard metric will probably ever be able to
predict the response of every pilot to an unexpectedturbulence upset.
Concluding Remarks
A quantitative hazard metric for airplaneturbulence response has been described. The metric is
intuitively and is intended to replace the subjective,
airplane-dependent Pilot Reports (PIREPS) in currentuse. A procedure for calculating the metric has beendescribed and demonstrated using preliminary values
for the fixed parameters defining the metric. Themetric has been applied to simulated discrete andcontinuous gust encounters and has been shown to givereasonable results. That is, the discrete gusts are
adequately described by the "peak" components of thehazard metric, and continuous turbulence is adequatelydescribed by the "sigma" component of the hazardmetric.
The fixed parameters defining the hazardmetric need to be more thoroughly checked before the
hazard metric is operational. The metric should also becompared to actual airplane responses (rather than
simulated responses as was done here) for severalencounters of real turbulence by instrumented airplanes.
The correlation is expected to be useable for most
modem transport airplanes. The defining parameters ofthe final hazard metric will be a compromise fordifferent gust shapes/flight conditions/airplanes/etc.
-6-
American Institute of Aeronautics and Astronautics
Theparametersthatneedtobeoptimized/ascertainedare:
(1) The number of rise times in the "peak"
hazard metric component calculations (3in above example)
(2) The values of the rise times over which
the peak gust amplitudes are calculated
(0.25, 1.0, and 4.0 in above example).(3) The best relationship between gust
amplitude and rise time for adjusting the
dimensional gust amplitudes of airplaneresponse (equation (3)).
(4) The time interval over which the metrics
are averaged and reported (2 minutes
preliminary suggested value).(5) The number of peak hazard metric values
that need to be reported. That is, whether
both positive and negative hazard metriccomponents need to be reported (as in
above example) or is the largest absolute
metric or the negative metric sufficient.
(6) The effect of spatial or temporalresolution (data rate) of the vertical gustmeasurements.
.
References
Fuller, J.R., "Evolution of Airplane GustLoads Design Requirements," Journal of
Aircraft Vol. 32, No. 2 March-April 1995
.
.
.
.
.
.
Soreide, David C., et al "Airborne Coherent
Lidar for Advanced In-Flight Measurement
(ACLAIM) Flight Testing of the LidarSensor," 9 th Conference on Aviation, Range,
and Aerospace Meteorology [for AmericanMeteorological Society], Sept I 1-15, 2000.
Cornman, Larry B, et al. "Real-TimeEstimation of Atmospheric Turbulence
Severity from ln-Situ Aircraft Measurements."Journal of Aircraft, Vol. 32, No. 1, January-
February 1995Chan, William; Lester, Peter F., and Bach,
Ralph E.: " Wingrove Parameter: A NewTurbulence Metric" Journal of Aircraft Vol 33,
No. 2, March-April 1996.Bass, Ellen J., et al. "Pilot Decision Aid
Requirements for a Real-Time TurbulenceAssessment System" The Tenth InternationalSymposium on Aviation Psychology.
Columbus, Ohio, May 2-6, 1999.
Jeppesen Sanderson Training Products.Federal Aviation Regulations/Aeronautical
Information Manual 2000. JeppesenSanderson Inc.
Stewart, Eric C., "A Study of AirlinePassenger Susceptibility to Atmospheric
Turbulence Hazards," AIAA Paper 2000-3978, August, 2000.
-7-
American Institute of Aeronautics and Astronautics
[Not r_rt ol
Jlgodthm]
Running RMS _1
computation interval=,4 seconds
A/C .S CL_d.. / /b_,I t
O'4.0(t)
(g's) I t HM, Average (g's)
reporting Interval - 2 minutes
HM=[HM a HM+
figure 3
figure 2 C_ Adjustf°r _ [ HM+'HM-/-_[ Incremental A_AmplitudesI tms_[ --W1 I(gslI_C"P°°"I MinimumMaximum.(g's)
r=O1S, 1,0, 4.0 secondsreporting interval - 2 minutes
Combine
Figure 1. Flow diagram of hazard metric calculation.
Measurement
at t = t I Least Squares line
_ (t 1)',_IA //_ r=4.00 ^.
Vertical I_A ' r=1'_OOk'_ J _'/ "_ J_V___ ._
gust velocity, fps V- '_ [----_ :i_,,-l- _ --_'tJ V X "- Time
" "\I _"................ Al"°(t 1) )I (typical}
I
Vertical
gust velocity, fps
Figure 2.
Measurement
at t = t 2 Least Squares line
I /aa(t2) r=l.00
r =0.25 :_ _, /
ooI
Illustration of incremental, dimensional gust amplitude calculations.
-8-
American Institute of Aeronautics and Astronautics
(A+)1.0
For HM+= _'--_" 0example
shown (Ao)4.0
HM.=-
1.0
A, 0non-dimensional
Maximum relativevalue
'...... _ ® (_'+)4.0A I ,_ I
(1,(A'+) 1. 0 )___
1 constant + 1g acceleration
Figure 3.
('_+).25
I I I ,,._,2.S 1,0 4,0
('_J.25 r, seconds
-1.o ® (_'J1.o
_nimum relative value
' A ', ® ( J4.o',
_I
constant-1 g acceleration
(4,(_. )4.0)
Graphical depiction of the terms involved in the peak values of'the hazard metric.
2°°t i_'
Wg , rps o _-2ooI i ,
1°° I , ,
o,_. o , fps 50_--'_'__01 i I
, i i i i i i
i
I I L I I I I
i
200, , ,
IAC25 • fPs 0_
-200 I i I ,
! ! ' T ! '
, i i ,! , !
I I I i I
2001 ........
A_.O, fps 0 " : ..... : " "-200 J , , , i , i , ,
200 .........
A4. 0 , fps 0
- 200 ' ' ' K , , J , J0 2 4 6 8 10 12 14 16 1'8
Time, seconds
2O
Figure 4. Incremental, dimensional gust amplitudes and running SIGMA for a discrete gust
9
American Institute of Aeronautics and Astronautics
Note: • 'sindicate mexlmum and minimums
acg, g's 0 ......... .... , ......
-5 , , , , I '
2_ ! ' ! ' I !cn'g's 11"-r :__ _ i..... av_,o.sz.a-.
o" /
51 i _6' ! ' ' ' , ,aaft,g's 0 I-------'__ : - " -
-5 { I 21o3 I L I i i i
average-1.18-HM_ .0"4. 0 , g's ..... ."_ . -: .... : - ..... : ........ . ..... : .
i " i ----q i ;I t I I
1 i i i i i i i i
HM.25 , g's 0 ..... i "i ! ! : :-51 i -1._s, • , i ,I I I
51, !_z9 ' ! ! ' ! 'HMI.o,g's 0 .... i . " : .......
-5 i i i i i
50_ I 0.71 ! I I _ !HM4.o , g's .....-5l 7°8 i _ , , , i
0 2 4 6 8 10 12 14 16 18 20
Time, seconds
Figure 5. Hazard metrics components for a discrete gust.
200 ! ! , , _ ! ! ! !
wg, fps 0 i .... " " . i !. : .......
-200
' I" fps ! " ' " !C_4. 0 ,
o , ; , i i200 ..........
A25 , fps 0
-200
200/ i i- T ' i ! --4' ' '
2ooI , _ , , , , JA;o,,ps o1-t-_-200 / I I I I I I I I I
0 1 2 3 4 5 6 7 8 9 10
Time, seconds
Figure 6. Incremental gust amplitudes and running SIGMA for Dryden turbulence.
-10-
American Institute of Aeronautics and Astronautics
Note: • 's indicate maximums and minimums
51 ' ' ! ' ! ! ' 2.59 , !/
21 .... ! ! ' ' ! /
O'n'g's 1I' ...... i ..... i "_" average'l"29=°'n t0 , , z , i
5725/ J , E J .A ^, , , #I---';
-5.72u u !
il ! ) "-_'_-_ ' '_ average-1.47_HM(_(_4.0, g's ................................. " .
I I I I
5f , , , , , , , ' _4 71 --
HM'25 ' g's-: _, _ , i -3.9; : , ,_J_
5 i i i i i i i i i
HM1.0,g's 0 " i i i ! ' :
-5 I I
_J_____ , .52 ' , ! ! ! , IHM4. o , g's ....... .-.39
-5 _ * , , I i 1 l i
0 1 2 3 4 5 6 7 8 9
Time, seconds
I10
Figure 7. Hazard metric components for Dryden turbulence
HMpeak, g'sRoar
• NT$O
A 1-courm
( acg )peak , g'sFigure 8. Comparison of the peak hazard metric components with simulated accelerations at the
center of" gravity
-II-
American Institute of Aeronautics and Astronautics
HMpeak, g's
o
the Dr _m'_ I_ DmlntaWnulm_
Figure 9. Comparison of the peak hazard metric components with the simulated accelerations atthe aft passenger cabin.
2.5 ;
HMo., g'sI
Figure 10.
0,5
i • X....O5 15 2,5
a n , g's
Sigma component of hazard metric for various types of turbulence.
-12-American Institute of Aeronautics and Astronautics
